KANSAS CITY, Mo. >> It took the biggest rally in franchise history for the Kansas City Chiefs to win their opener.

After the Chiefs dug out of a three-touchdown hole, Alex Smith dived for a score on the first possession of overtime Sunday, giving his team a heart-stopping 33-27 win over the San Diego Chargers.

Smith threw for 363 yards and two touchdowns, the second a back-shoulder fade to Jeremy Maclin with just over 9 minutes left in the fourth quarter. The Chiefs, at one point trailing 24-3, had trimmed their deficit to 27-17 and energized a crowd that had begun thinning at halftime.

Cairo Santos kicked a 33-yard field goal a few minutes later. Then, after forcing a three-and-out, Spencer Ware finished a four-play drive with a touchdown plunge to knot the game at 27.

It took Kansas City 10 plays to march 75 yards in overtime. Smith finished it with his keeper on third-and-goal from the 2-yard line as the Chiefs flooded off their bench to celebrate.

Ware finished with 70 yards rushing and had seven catches for 129 yards, giving the Chiefs a big boost without Jamaal Charles. The four-time Pro Bowl running back is still recovering from surgery last season to repair his ACL and was inactive Sunday.

Philip Rivers threw for 243 yards and a touchdown, and Melvin Gordon scored the first two TDs of his career. But the Chargers were unable to keep any drives going in the fourth quarter, when the Chiefs were charging to their NFL-leading 11th consecutive regular-season victory.

The collapse came after San Diego after wide receiver Keenan Allen left in the second quarter with what appeared to be a serious knee injury. He had six catches for 63 yards.

Still, the Chargers managed a 21-3 halftime lead, and it appeared coach Mike McCoy’s team was well on its way toward ending an eight-game skid against AFC West rivals.

Everything changed in the fourth quarter.

The Chargers were leading 27-10 when Josh Lambo missed a 54-yard field goal, and the momentum swung toward Kansas City. Smith calmly completed six passes and marched his team 56 yards to the end zone.

Santos added his field goal, Ware added his touchdown and it was off to overtime.

BLACK POWER

Chiefs cornerback Marcus Peters held a black-gloved fist aloft during the national anthem in a salute reminiscent of Tommie Smith and John Carlos at the 1968 Mexico City Olympics. Peters said this week he was in agreement with 49ers quarterback Colin Kaepernick’s stance on social injustice.

Peters did link his left arm with his teammates as country singer Trace Adkins performed the anthem. The Chiefs said in a statement they decided to lock arms in a show of solidarity.

MISSING NAMES

The Chiefs played without star pass rusher Justin Houston, who could be out until November as he recovers from ACL surgery in February. The Chargers were without defensive end Joey Bosa, the third pick in April’s draft, who remained on the exempt list after a lengthy holdout.

INJURY REPORT

Allen missed the final eight games last season with a lacerated kidney, and now could be out the rest of this season. He never put weight on his right knee after going down Sunday.

Chiefs linebacker Sam Barrington left in the second half with a hamstring injury.